Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces (V/ρ) to viscous forces (μ/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions.
Reynolds numbers frequently arise when performing dimensional analysis of fluid dynamics and heat transfer problems, and as such can be used to determine dynamic similitude between different experimental cases. They are also used to characterize different flow regimes, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce random eddies, vortices and other flow fluctuations.
Reynolds number is generally defined as: Re=ρVL/μ
where: V is the mean fluid velocity in (SI units: m/s); L is the characteristic length of the structure (m); μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2); and ρ is the density of the fluid (kg/m3)
For any shape, the parameter that is used as the characteristic length L is not given explicitly by physics, but rather is chosen by convention (and usually subscripted after the ‘Re’).
In boundary layer flow over a flat plate, experiments can confirm that, after a certain length of flow, a laminar boundary layer will become unstable and become turbulent. This instability occurs across different scales and with different fluids, usually when Rex˜5 105, where x is the distance from the leading edge of the flat plate, and the flow velocity is the ‘free stream’ velocity of the fluid outside the boundary layer. In conventional aerodynamics, the following approximate ranges apply for Reynolds number:
Extremely low: 1,000≦Re≦20,000
Very low: 20,000<Re≦200,000
Conventional low: 200,000<Re≦1,000,000
Intermediate: 1,000,000<Re≦5,000,000
High: Re>5,000,000
Fans are widely used for personal, industrial and automotive cooling, ventilation, vacuuming and dust removal, inflating, etc. Ducted, or shrouded, fans have for many years been used for propulsion of airboats, air-cushion vehicles, airships and model aircraft. They are also touted as the primarily propulsive system for so-called personal air vehicles, a number of which are under intense development (e.g. White, 2006; and Yoeli, 2002). Their main advantages are high static thrust and propulsion efficiency, while the duct acts to reduce blade noise and improve safety. The main factor limiting the performance of these blades is boundary layer separation, where the flow detaches from the blade surface. This leads to dramatic losses in performance and severe increases in noise and vibrations. The typical Reynolds number range is conventional low to intermediate.
In recent years, ducted fans have received renewed attention, particularly for the propulsion of small-scale (typically ˜500 mm) unmanned air vehicles (Fleming et al, 2003; Guerrero et al, 2003). In addition, there is a trend toward the design of even smaller air vehicles, known as “micro air vehicles” (MAVs; maximum dimension typically between 7.5 cm and 15 cm), for a variety of military and civil applications. One consequence of these smaller scales and relatively low tip speeds is a reduced fan blade Reynolds number, typically less than 50,000. At these Reynolds numbers, boundary layer transition does not occur and the boundary layer is susceptible to separation, which can result in a catastrophic loss of propulsion. The best performing blade profiles are thin, curved sections which do not produce a large pressure ΔP across the disk since leading-edge separation occurs at relatively low inflow angles.
A rapidly growing application of fans and ducted fans is their ubiquitous use for the cooling of modern high-speed computer systems at large scales and also at small scales such as on computer chips, motherboards and power supplies. Large scale server farms, which are collections or clusters of computer servers, are increasingly being used instead mainframe computers by large enterprises. The performance server farms (typically thousands or tens of thousands of processors) are typically limited by the performance of the cooling systems. At the small scales, typically, a fan blows air across a heat-sink that is attached to a particular component, such as a CPU. In modern designs, fan speed can be controlled based on a feedback principle and this is generally referred to as active cooling. However, modern high-speed processors require continuously greater cooling and this is generally accomplished using larger heat sinks and more powerful fans running at higher rpm. Apart from physical size limitations, these fans are increasing noisy and require greater input power. In fact, the noise generated by fans that are used to cool high-end processors, particularly within a small physical computer sizes, is often objectionable to the user.
The above mentioned problems were negotiated by designing more efficient blade sections, but this optimization process has now reached its limit.
Achieving sustained flight of micro air vehicles (MAVs) brings significant challenges due to their small dimensions and low flight speeds. For so-called mini air vehicles, which operate in the 10,000<Re<300,000 range, efficient systems can be designed by managing boundary-layer transition via passive tripping at multiple locations. However, at Reynolds numbers routinely experienced by MAVs (Re<100,000), conventional low-Reynolds-number airfoils perform poorly or generate no useful lift. Some of the best-performing airfoils in this Re range are cambered flat plates and airfoils with a thickness-to-chord ratio of approximately 5%. There are various definitions for MAY dimensions and weight, although one common definition refers to large (b˜15 cm and m˜90 g) and small (b˜8 cm and m˜30 g) MAVs. To maximize wing area, these vehicles typically have low-aspect-ratio (AR) wings (1<AR<2) for which typical Reynolds numbers during loiter are in the range of 20,000<Re<80,000, based on the aforementioned specifications. Innovative designs with larger-aspect-ratio wings can result in an even lower Reynolds number range.
The challenge of developing useful lift intensifies with yet smaller vehicles required to fly at even lower flight speeds. This includes the development of so-called nano Unmanned air Vehicles (UAVs) for which the missions include flying within confined areas. These are commonly termed Nano Air Vehicles (NAVs) and are defined as weighing less than 10 g, with dimensions smaller than 7:5 cm, and speeds between 0.5 and 7:5 m/s.
The significant difficulty associated with generating lift at Re<20,000 has led many to pursue biologically inspired approaches in which the flight of small birds and insects is mimicked to a greater or lesser degree.
It is well known that a fan (or wind pump) can also be used as a turbine. The most common of these is the horizontal axis (axial flow) wind turbine, where wind turns the turbine blades that, in turn, drive a generator.
Patent application WO07106863A; titled “Methods and apparatus for reducing noise via a plasma fairing”; to Thomas Flint; discloses a plasma fairing for reducing noise generated by, for example, an aircraft landing gear is disclosed. The plasma fairing includes at least one plasma generating device, such as a single dielectric barrier discharge plasma actuator, coupled to a body, such as an aircraft landing gear, and a power supply electrically coupled to the plasma generating device. When energized, the plasma generating device generates plasma within a fluid flow and reduces body flow separation of the fluid flow over the surface of the body.
US application 20020195089A; titled “Self contained air flow and ionization method, apparatus and design for internal combustion engines” to Zetmeir Karl; disclosed method to enhance the performance of internal combustion engines by the creation of a swirling vortex, using principles of electrostatics in using tribology and coulomb forces, the utilization of dielectric properties of polymers in an air driven rotating electrophorus and the chemistry of enhanced combustion gases and combustion itself in a single self-contained apparatus and does so without the convention and application of external voltage
US application 20040195462; titled “Surface plasma discharge for controlling leading edge contamination and crossflow instabilities for laminar flow”; to Fedorov Alexander and Malmuth Norman; discloses a system and method for controlling leading edge contamination and crossflow instabilities for laminar flow on aircraft airfoils that is lightweight, low power, economical and reliable. Plasma surface discharges supply volumetric heating of the supersonic boundary layers to control the Poll Reynolds number and the cross flow Reynolds number and delay transition to turbulent flow associated with the leading edge contamination and crossflow instabilities.
US application 20040118973; titled “Surface plasma discharge for controlling forebody vortex asymmetry” to Federov Alexander et. al.; discloses a system and method for rapidly and precisely controlling vortex symmetry or asymmetry on aircraft forebodies to avoid yaw departure or provide supplemental lateral control beyond that available from the vertical tail surfaces with much less power, obtrusion, weight and mechanical complexity than current techniques. This is accomplished with a plasma discharge to manipulate the boundary layer and the angular locations of its separation points in cross flow planes to control the symmetry or asymmetry of the vortex pattern.